Lesson 4.1.1 4-7. See graph at right. x = 0 and x = 4 4-8. a: x = 5 or x = –3 b: m = 35 c: no solution d: x = 7 4-9. a: y = 0 b: x = 0 4-10. a: Combining the equations leads to an impossible result, so there is no solution. b: See graph at right. c: There can be no intersection because the lines are parallel. When assuming there is an intersection, students will find that their work

results in a false statement. 4-11. This is a scalene triangle, because the sides have lengths 29 , 17 and 20 . 4-12. a: 63 b: 0 c: n3 –1 d: Neither; answers will vary. 4-13. a: (x!2)(x+6)(x+4)(2x+3) b: 2x+1x!5 c: 9m+27m+3 = 9 d: n+3n–1 4-14. a: 0–2 times b: 0–4 times c: 0–4 times d: 1-3 times if you consider parabolas that open up or down. 0-4 times if you

consider rotated parabolas.

y

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x

Lesson 4.1.2 4-22. Answers will vary. 4-23. See graph at right. x = 3 and x = 6

4-24. a: x = 15 b: x = 73 or x = –5

4-25. The lines intersect at the point (2, 6).

Ted will solve the system algebraically by setting 18x – 30 = –22x + 50. 4-26. a = 18.5, b = 5.5 4-27. x = 13, x = 5 is extraneous 4-28. x = 36 b: x = 20 2 or x ≈ 28.28 4-29. See graph at right. x = 1 and x = 3; No. 4-30. a: 12 (x ! 2)

3 +1= 2x2 ! 6x ! 3 , x = 0 or x = 4

b: x = 6 is also a solution.

c: 12 (x ! 2)3 +1= 0 , x ≈ 0.74

d: Domain and range of f(x): all real numbers, domain of g(x): all real numbers, range of g(x): y ≥ –7.5

4-31. a: x = –3 b: x = 1 or x = 3 c: x = –8 or x = 13 d: x = 1.2 4-32. a: y = 5

3 x – 4 b: m2 = Fr2Gm1

c: m = 2Ev2

d: y = ± 10 ! (x ! 4)2 +1

4-33. (a + b)2 = a2 + 2ab + b2 , substitute numbers, etc. 4-34. a: See graph at top right. b: See graph at bottom right. c: Graph (b) is similar to graph (a), but is rotated 90º clockwise. d: (a) D: all real numbers, R: y ≥ 0; (b) D: x ≥ 0, R: all real numbers 4-35. a: 21.00 b: 117.58

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x 5

5

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Lesson 4.1.3 4-40. a: (–2, –11); The lines intersect at one point. b: infinite solutions; The equations are equivalent. c: (2, 45), and(–1, 3); The line and parabola intersect twice. d: (3, 6); The line is tangent to the parabola. 4-41. a: y = 3 or y = –5 b: x = – 994 c: y = 1 d: x = –13 4-42. a: E t(n) = !2 + 3n ; R t(0) = !2,!t(n +1) = t(n)+ 3 b: E t(n) = 6(12 )

n ; R t(0) = 6,!t(n +1) = 12 t(n)

c: t(n) = 10 – 7 d: t(n) = 5(1.2)n e: t(n) = 1620 4-43. 19.79 feet 4-44. a: m = – 65 , b = (0, –7) b: m = 3

2 , b = (0, –5) c: m = 2, b = (0, –12) 4-45. a: not a function; D: –3 ≤ x ≤ 3; R: –3 ≤ y ≤ 3 b: a function; D: –2 ≤ x ≤ 3; R: –2 ≤ y ≤ 2 4-46. (–7, 11)

Lesson 4.1.4 4-51. 4c + 5p = 32, c + 8p = 35, cylinders weigh 3 oz. and prisms weigh 4 oz. 4-52. Yes. No. Any value of x such that –3 ≤ x ≤ 2 is a solution. 4-53. a: x = 4 b: x = 6 c: x = 6 d: x = 3

2 4-54. a: (4, –6) b: (4, –6) c: 3

2 , –94( )

4-55. a: b: 4-56. B 4-57. a: See graph at right. b: x ≈ 0.71

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Lesson 4.2.1 4-65. a: boundary point x = –4 b: boundary points x = 4, – 32 4-66. a: –4 < x < 1 b: x ≤ –4 or x ≥ 1 c: –1 < x < 4 d: x ≤ –1 or x ≥ 4 e: –1 < x < 4 f: x ≤ –1 or x ≥ 4 4-67. a: y = –3x + 8 b: y = –x – 12 4-68. a: No real solutions b: y = 7, y = 13

3 is extraneous 4-69. a: 3x2+x!3

2x3+9x2!5x b: 3x!52x+3 c: x+4

4x!3 d: m+5m+4 4-70. x = !6 + 4 6 or x = !6 ! 4 6 4-71. a: x(b + a) b: x(1 + a) c: a

x+1 d: x–ba 4-72. See graph at right. a: Rectangle; perpendicular lines or slopes. b: (1, 4), (–3, –3), (–5, 1), (3, 0) 4-73. a: –5 < x < 13 b: x ≥ 250 or x ≤ –70 c: 32 ! x !

72

4-74. a: C = 800 + 60m b: C = 1200 + 40m c: 20 months d: 5 years 4-75. a: input x, output x b: Replace x with c in first function machine resulting in c – 5 , then substitute this

expression for x in the second function machine, yielding 6(c!5)+82 = 3c !11 . Substitute this a third time in the final machine, giving (3c!11)+113 = c .

4-76. a: x–3

3x–14 b: 2x–1x+1 4-77. (1, 12) and (–5, 42) 4-78. a: y = 1

2 x – 2 b: y = 2x + 2

x

y

Lesson 4.2.2 4-83. x = –2, y = 3, z = –5; Solve the system to two equations with x and y, then

substitute these values into the third equation to find z. 4-84. a: x ≤ 4 b: x < –6 or x > 6 4-85. red = 10 cm, blue = 14 cm 4-86. The points on the line y = 2x – 2 are excluded from the solution region of y < 2x –2. 4-87. a: y = 1

3 x – 4 b: y = 65 x –

15 c: y = (x + 1) 2 + 4 d: y = x2 + 4x

4-88. y = 0, x = 0 4-89. 2.11 feet

Lesson 4.2.3 4-92. There is no solution, so the lines are parallel. 4-93. See graph at right. a: A square, justifications will vary. b: (0, –3), (4, 1), (–4, 1), (0, 5) c: 32 square units. 4-94. a: x < 13 b: 5! 57

4 " x " 5+ 574 or !0.637 " x " 3.137

4-95. a: no solution b: y ≈ 4.3 or 10.7 4-96. (25, –3) a: x2 + 3y = 16 and x2 ! 2y = 31 b: The solutions to the new system are (5, –3) and (–5, –3). 4-97. a: See graph at right; y = –2x +8 b: 63.43º or 116.57º

–5 0 5 –6 x 0 6

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13 –1 0 3

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y

Lesson 4.2.4 4-99. a: y = 1

2 (x + 3)2 ! 2 b: y = x +5 c: x = 1 or x = –5

d: (1, 6) and (–5, 0) e: x < –5 and x > 1 f: x = –1 or x = –5 g: x = –1 h: Answers will vary. 4-100. y ! 3x + 3 , y ! 0.5x " 2 , y ! "0.75x + 3 89784 4-101. a: x ≤ 1 or x ! 7

3 b: x < 3 4-102. a: b: c: 4-103. 60º 4-104. a: y > 3x –3 b: y < 3 c: y ! 3

2 x – 3 d: y ! x2 – 9 4-105. a: w = 0 or w = –4 b: w = 0 or w = 25 c: w = 0 or w = 6  

0 1 2 x 11

2 3 x

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